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Title Strain Softening of Siltstones in Consolidation Process
Author(s) Kamiya, Nana; Zhang, Feng; Fukuoka, Junichi; Kato, Yushi;Lin, Weiren
Citation MATERIALS TRANSACTIONS (2020), 61(6): 1096-1101
Issue Date 2020-06
URL http://hdl.handle.net/2433/265079
Right © 2020 The Society of Materials Science, Japan; 発行元の許可を得て登録しています.
Type Journal Article
Textversion author
Kyoto University
2
Manuscript number 1
2
Strain Softening of Siltstones in Consolidation Process 3
4
Nana Kamiya1*, Feng Zhang2, Junichi Fukuoka3, Yushi Kato4, and Weiren Lin1 5
6
(Author’s Affiliation) 7
1 Graduate School of Engineering, Kyoto University, Kyoto Daigaku Katsura, Nishikyo-ku, Kyoto 8
615-8540, Japan 9
2 Department of Civil Engineering, Nagoya Inst. of Tech., Gokiso-cho, Showa-ku, Nagoya 466-8555, 10
Japan 11
3 Department of Civil Engineering, Nagoya Inst. of Tech., now at Hanshin Expressway Company 12
Limited, Nakanoshima, Kita-Ku, Osaka 530-0005, Japan 13
4 Department of Civil Engineering, Nagoya Inst. of Tech., now at Aichi Prefectural Government, 14
Nishiyanagihara-cho, Tsushima 496-8533, Japan 15
16
* Graduate Student, Kyoto University 17
18
Abstract 19
Strain softening is the mechanical behavior of soil and rock materials and is 20
important in understanding soft rock foundation. To investigate the mechanical behavior 21
of siltstone, a sedimentary soft rock, consolidation tests using constant-strain rate 22
loading were conducted using the consolidation ring to constrain lateral deformation. 23
Using Quaternary siltstones distributed in the Boso Peninsula, central Japan as 24
specimens, strain softening in the consolidation process was confirmed in some 25
formations using two test machines at Kyoto University and Nagoya Institute of 26
Technology. Just before the yielding, stress decreased suddenly at increasing strain. The 27
stress at the time of the softening differed even for specimens taken from the same 28
formation. Furthermore, micro-focus X-ray CT images taken before and after the tests 29
3
indicated that the specimens had no macro cracks inside. This suggests that strain 30
softening is not due to brittle failure in local areas but due to the softening of the 31
framework structure of the siltstone itself. 32
33
Keywords: Consolidation test, Strain softening, Sedimentary soft rock, Siltstone 34
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1. Introduction 59
The mechanical behavior of rock masses comprising hard rocks is based on 60
geological weak planes such as joints, fractures and faults. However, that of soft rocks 61
is dominated by the mechanical properties of the rock itself. Because soft rocks have 62
different physical properties to hard rocks, it is essential to understand the mechanical 63
behavior of soft rocks when tunnels and huge structures are constructed in these. 64
Neogene and Quaternary sedimentary rocks generally considered as soft rocks are 65
distributed throughout Japan. Sedimentary soft rocks are softer than hard rocks and their 66
physical properties lie between those of soil and rocks1). 67
Understanding strain softening is important for understanding the mechanical 68
characteristic of soft rocks. In general, strain increases as stress increases with loading. 69
However, strain softening is a phenomenon in which the stress does not increase with 70
loading after the stress reaches a certain value, or the strain increases significantly for a 71
small stress increase. The phenomenon is often observed at shearing of dense sands, 72
over-consolidated clay and soft rocks, and is closely related to the progressive failure 73
discussed in various geotechnical problems. Mechanical models using numerical 74
analysis have been calculated2), 3). Triaxial compression tests have been conducted using 75
sedimentary soft rocks such as porous tuff4), 5) and diatomaceous soft rocks6), which 76
have clarified their mechanical properties. Akai et al.4) and Adachi et al.5) conducted 77
triaxial compression tests using Oya stone, a porous tuff and clarified that the 78
elastoplastic behavior, dilatancy and time dependence of the soft rock are characterized 79
by the intermediate properties between soft soil and hard rock. Adachi and Oka7) 80
constructed constitutive equations for elastoplastic behavior of strain softening of soft 81
rocks and considered that strain softening is caused by both localization of deformation 82
and softening of the rock material itself. They compared the models with results of 83
experiments and described that the phenomena in both the models and results were 84
consistent. Furthermore, Zhang et al.8) and Iwata et al.9) improved these constitutive 85
equations and compared them with actual phenomena. However, there are currently no 86
reports of strain softening observed in consolidation tests. 87
5
There are a number of ways to view the term “strain softening.” When the softening 88
occurred during loading of the rock material, shear bands simultaneously form in the 89
loaded specimens. Therefore, this softening is not “strain softening”, but is recognized 90
as a phenomenon caused by plastic hardening of the material and localization of 91
deformation such as formation of shear bands. Debate around this was mostly in the 92
1980s and 1990s, but has not yet been finalized. Considering this background, we 93
focused on the softening behavior of soft rocks and performed consolidation tests to 94
verify whether this phenomenon is an essential property of the ground material itself 95
(that is, an element property) or a boundary variation of deformation localization. 96
Kamiya et al.10) conducted consolidation tests using sedimentary soft rocks taken from 97
the Boso Peninsula to elucidate the generation of abnormal pore water pressure during 98
development of the forearc basin. Consequently, a phenomenon that seems to be strain 99
softening was confirmed in advance. Therefore, consolidation tests were performed 100
with the large number of samples taken from Quaternary layers in the Boso Peninsula to 101
confirm and elucidate strain softening. In this study, the reproducibility of the 102
phenomenon was also confirmed using different equipment. 103
104
2. Experimental materials 105
Neogene siltstone is relatively weak as a rock and is generally classified as a soft rock. 106
Natural siltstones have a consolidation fabric in which clay minerals are oriented 107
parallel to the geological bedding plane, include volcanic crustics such as pumice and 108
scoria and fine particles derived from microfossils like foraminifera and diatoms. 109
Additionally, they have been hardened by diagenesis and cementation depending on the 110
sedimentary environment. However, a high-pressure consolidation test of the siltstone 111
under drain conditions shows a consolidation curve that is very similar to that of 112
over-consolidated clay because its porosity is relatively high11), 12). Experimental 113
samples used in this study are siltstones taken from central Boso Peninsula in Chiba 114
Prefecture, central Japan. The forearc basin sediments are distributed in the middle and 115
northern part of the Boso Peninsula (Figure 1). The Boso forearc basin is divided in the 116
6
Miocene to Pleistocene Miura Group and Kazusa Group. The boundary between the two 117
groups is the Kurotaki Unconformity, a large-scale geological boundary distributed 118
from east to west. The Kazusa Group comprises alternation of sand and mud without 119
hydrothermal metamorphism and includes many volcanic tuff layers. Sediment 120
thickness in the eastern Kazusa Group is greater than in the western part and some of 121
the lower formations of the Kazusa Group (Ohara, Namihana and Katsuura formations) 122
are distributed only in the eastern part of the basin. Consolidation tests were performed 123
using siltstones taken from the Kiwada (BosC32), Otadai (BosC10) and Ohara 124
(BosC26) formations. The sedimentary age of these formations is approximately 125
100-150 million years14), 15). 126
Block samples were taken from the outcrop except cracked and weathered parts. 127
Blue-gray fresh siltstones were cut out in a block to fix direction. They were formed 128
into a 27-mm-diameter cylinder with an axis perpendicular to the geological bedding 129
plane and the curved surfaces of the cores were polished to a diameter of 25 mm using a 130
cylindrical grinder. The core samples were cut to a height of ~21 mm using a rock cutter 131
and the top and bottom surfaces were polished using a surface grinder so that both ends 132
are parallel and the cores were 20 mm high. The specimens were immersed in tap water 133
in a vacuumed desiccator to saturate highly. 134
Density and void ratio of the specimens were measured using the buoyancy method. 135
Specifically, the wet and submerged weights of the specimens were measured before the 136
tests. The specimens were dried in an oven at 60°C for four days after the tests and the 137
dry weight was measured. The equations for calculating soil particle density ρg, void 138
ratio e and porosity φ of each specimen are as follows: 139
140 𝜌" = 𝑀%&'/(𝑀*+, − 𝑀*.,+&) − (𝑀*+, − 𝑀%&'), (1) 141 142 𝑒 = [ 𝑀*+, − 𝑀*.,+& − 𝑀%&' 𝜌"]/[𝑀%&' 𝜌"] and (2) 143 144 𝜙 = (𝑀*+, − 𝑀%&')/(𝑀*+, − 𝑀*.,+&), (3) 145
146
7
where M is weight; ρ is density; and subscript dry and wet of M mean weights of dry 147
and wet specimen measured in atmosphere, respectively, but water is weight of the wet 148
specimen measured under submerged condition. The specimens were subjected to 149
micro-focus X-ray CT imaging before and after the consolidation tests and the internal 150
structures were observed. CT images were acquired using HMX225-ACTIS+5 (TESCO 151
Corp.) before the test and Xradia (ZEISS Corp.) after the test. This equipment is owned 152
by Kochi University, Japan. The imaging conditions were a tube voltage of 90 kV, tube 153
current of 50 µA and spatial resolution of ~35 µm. 154
155
3. Experimental procedure 156
Constant strain rate consolidation tests were performed with a uniaxial compression 157
apparatus using a rigid stainless-steel ring in a consolidation test chamber (Figure 2). 158
The specimens were fitted into the ring to avoid lateral expansion during loading. To 159
reduce friction on the curved surfaces of the specimen, double Teflon sheets between 160
which silicon grease was applied were sandwiched between the specimen and 161
consolidation ring. The loading speed was controlled at a constant-strain rate of 162
0.05%/min and the maximum loading stress was 80 MPa. Unloading was performed at 163
a constant-strain rate of 0.10%/min after the loading, which was completed when the 164
displacement change stopped. The tests were conducted under drain conditions. The 165
upper end of the specimen was open and connected to a volume meter to measure 166
drained water volume to evaluate the specimen’s volume change during the 167
consolidation test. The lower end was closed and pore water pressure was measured 168
here. We used two apparatuses owned by Kyoto University (Figure 2) and Nagoya 169
Institute of Technology, Japan to analyze the reproducibility of consolidation behavior. 170
Both apparatuses have the almost same system and specifications. Axial load, axial 171
displacement, volume of drained water from upper end of the specimen and pore water 172
pressure at the lower end of the specimen were measured at intervals of 1 second during 173
the tests. 174
Using measured data such as axial load and pore water pressure, consolidation curves 175
8
were drawn in semilogarithmic graphs with the vertical axis representing the void ratio 176
and the horizontal axis representing the logarithm of stress (Figure 3a). Stress p on the 177
horizontal axis was calculated from the axial compressive stress σ and pore water 178
pressure u as follows 16). 179
180 𝑝 = 𝜎 − (2𝑢/3) (4) 181
182
The consolidation yield stress was estimated based on the Mikasa’s graphical method17) 183
using the consolidation curves. The drawing method is as follows. First, two points are 184
taken at the steepest slope of the consolidation curve and Cc is obtained from Equation 185
(5) using the respective coordinate values. Then, Cc’ is estimated from Equations (6) and 186
Cc” from (7) (Figure 3b). 187
188
𝐶: = (𝑒. − 𝑒;)/𝑙𝑜𝑔(𝑝;/𝑝.) (5) 189
190 𝐶:@ = 0.1 + 0.25𝐶: (6) 191
192 𝐶:" = 0.5𝐶:@ (7) 193
194
Second, point A, where the consolidation curve intersects the straight line with slope Cc’ 195
is drawn. Then, point B is determined, which is the intersection of the straight line with 196
the slope of Cc” through point A and the extension line of the straight part representing 197
the steepest slope of the normal consolidation line. Finally, the horizontal coordinate 198
value of point B is considered to be the consolidation yield stress pc (Figure 3b). 199
200
4. Results 201
Figure 4 shows the consolidation curves for each specimen. All specimens yielded 202
and the consolidation curves showed over- and normal-consolidation areas. Some 203
specimens’ stress dropped rapidly before yielding (arrows in Figure 4a and c). The 204
consolidation yield stresses were calculated based on Mikasa’s graphical method; the 205
9
results are shown in Table 1. When the consolidation curves show a rapid stress drop, 206
the tangents were drawn using the consolidation curves after the rapid stress drop. 207
The test for BosC32, taken from the eastern Kiwada Formation, was conducted with 208
apparatus owned by Kyoto University (Figure 4a). The rapid stress drop was confirmed 209
immediately before yielding, which occurred when the stress was approximately 12.3 210
MPa. The initial void ratio and consolidation yield stress of BosC32 were 0.91 and 7.0 211
MPa, respectively. 212
Consolidation tests for the samples taken from the Ohara Formation (BosC26) and 213
the western Otadai Formation (BosC10) were performed using two different 214
apparatuses owned by Kyoto University and Nagoya Institute of Technology. Two 215
specimens were formed from the same block sample and each test was performed using 216
the same procedure with each apparatus. The consolidation curve of BosC10-K shifted 217
to a decreased void ratio, which matched that of BosC10-N (Figure 4b). The 218
consolidation yield stress was 7.6 MPa for BosC10-N and 8.0 MPa for BosC10-K, 219
which are similar. Considering that the initial void ratio was 0.74 for BosC10-N and 220
0.69 for BosC10-K, the difference in that is 0.05, which indicates a discrepancy in the 221
consolidation curve, this explains the difference in the initial void ratio. Basic physical 222
properties such as porosity and soil particle density vary among specimens even in the 223
same geological layer because of the inhomogeneity of natural rocks. The void ratio 224
difference of ±0.05 can be considered a natural variation. The consolidation curves for 225
both specimens, BosC10-N and BosC10-K, were drawn smoothly from the beginning of 226
loading to the completion of unloading, which means that rapid stress drops were not 227
confirmed. 228
The consolidation curves of BosC26-N and BosC26-K taken from the Ohara 229
Formation agree well with each other and both show the rapid stress drops just before 230
yielding (Figure 4c). Considering the strain-stress relationship around the stress drop 231
point, the values of stress (p) at which the rapid stress drop occurred were 232
approximately 12.3 MPa for BosC26-N and 15.0 MPa for BosC26-K (Figure 4d). The 233
consolidation yield stress (pc) of BosC26-N was 9.4 MPa and that of BosC26-K was 234
10
10.3 MPa, which means that pc of BosC26-K was about 10% larger than that of 235
BosC26-N. The initial void ratio was 0.99 for BosC26-N and 0.97 for BosC26-K. 236
Figure 5 shows micro-focus X-ray CT images of BosC26-N taken before and after 237
the test. Although small white spots were observed inside the specimen before the test, 238
there were no large particles such as microfossil and cracks. This means that this 239
specimen is relatively homogeneous siltstone. The small white spots are microfossils or 240
microparticles of volcanic ash. The specimen was deformed during the test and the 241
center part of the upper face was raised in a convex shape after the test. This 242
deformation likely formed because the porous stone was softer than the surrounding 243
stainless-steel part. However, CT images of the specimen that experienced high stress 244
during the test indicated that cracks formed by deformation do not distribute in the 245
specimen. Although strain softening of soft rock in the constant-strain rate consolidation 246
test was not reported in previous studies, this study confirmed this phenomenon. 247
248
5. Strain softening 249
Consolidation tests were conducted on five samples in this study; three samples 250
showed the rapid stress drop just before yielding. Consolidation tests for two specimens 251
(BosC26-N and BosC26-K) from the Otadai Formation sample were performed using 252
the apparatus owned by Kyoto University and Nagoya Institute of Technology, 253
respectively. Similar stress reductions were observed in both tests, which suggested that 254
this rapid stress drop was reproducible. 255
The rapid stress drop confirmed in this study can be regarded as a real strain 256
softening because no strain localization could be confirmed within all specimens. In soil 257
materials, unsaturated soils exhibit significant strain softening. Decreased strength due 258
to a reduction in meniscus water is a cause of strain softening18). Strain softening of the 259
rock materials has been modeled in many elastoplastic constitutive equations, in which 260
the softening is generally considered to be related to a decrease in stiffness and a 261
reduction in yield surface5). In laboratory tests, however, softening behavior observed in 262
so called element tests usually always accompanied by the formation of shear band 263
11
within the ‘element specimen’, which, in a sense, means that the so called element test 264
is no longer an element test. Therefore, majority of the researchers related to 265
constitutive modeling7) usually regarded the strain softening of rock materials is just an 266
average behavior of localized deformation of shear band together with a stress reduction 267
process in other region of the specimen, even if the rock material itself is strain 268
hardening. In present research, however, X-ray CT images of BosC26-N before and 269
after the test showed that particularly large particles such as pumice and fossils were not 270
contained in the specimen. Additionally, micro cracks like brittle fractures were not 271
found in the specimen after the test. Therefore, it was suggested that the strain softening 272
observed in this study was attributable to softening of the siltstone itself. 273
Generally, siltstone has a relatively high clay mineral content. Because the friction 274
coefficient of some clay minerals such as smectite is small19), 20), the mineral component 275
of siltstone and their mechanical behavior might be related to strain softening. However, 276
the Otadai and Kiwada formations contain insignificant amounts of montmorillonite, 277
which is a type of smectite21). XRD analysis was performed for the specimens used in 278
this study (BosC32, 10-K and 26-K) and suggested that the clay mineral content is not 279
significantly high. 280
The samples used in this study are siltstone taken from the forearc basin, whose 281
development is related not only to consolidation but also tectonic effects such as 282
horizontal compaction accompanied with plate subduction. Therefore, it is possible that 283
the strain softening confirmed in this study reflects the micro cracks and internal 284
structure that developed during siltstone formation. In the future, the micro structure of 285
the specimen immediately after strain softening should be observed, which would 286
enable elucidation of the softening. 287
288
6. Conclusion 289
As a first step to elucidate consolidation yielding, which is one mechanical behavior 290
of siltstone, consolidation tests using consolidation rings were conducted for siltstone 291
from the Boso Peninsula, Chiba Prefecture, central Japan. Strain softening was 292
12
confirmed in the consolidation process of some specimens. This softening occurred 293
immediately before yielding, but the stress values at softening differed even in 294
specimens from the same block sample. Micro-focus X-ray CT images of the specimens 295
were taken before and after the tests. Because no cracks were observed in the specimens 296
after the tests, it is unlikely that the softening occurred because of local brittle failure. 297
Therefore, softening is precipitated by softening of the framework structure of the 298
siltstone itself; this phenomenon is defined as strain softening. 299
To understand the strain softening mechanism, the presence of cracks should be 300
confirmed by observation of the microstructure in the specimen immediately after the 301
strain softening. The strain softening observed in this study should be reproduced by a 302
numerical model and the constitutive equation to elucidate ground mass behavior, such 303
as how strain softening affects the deformation of the ground. 304
305
Acknowledgments 306
We thank Dr. Yuzuru Yamamoto and Dr. Masayuki Utsunomiya for advices and 307
assistance with sampling in the field. We are also grateful to Dr. Hirose Takehiro and Dr. 308
Osamu Tadai for support with the micro-focus X-ray CT images. Finally, we appreciate 309
Prof. Katsuaki Koike and Yu Shimoji for assistance with the XRD analysis. This 310
research was financially supported by a Grant-in-Aid for Young Researchers from the 311
Association for Disaster Prevention Research, Japan. 312
313
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Hiro: Abstruct of the 46th Jpn. Soc. Civ. Eng. (Kobe Japan, July), 219 (2011). 327
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Tectonophys. 710–711 (2017) 69–80. 333
13) K. Koike: J. Geol. Soc. Jpn. 57 (1951) 143–156. 334
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M. Chester, N. Eguchi, S. Toczko, Expedition 343 and 343T Scientists: Science. 342 344
(2013) 1211-1214. 345
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Captions List 351
Table 1 Basic physical properties and results of the siltstone used in this study. For the 352
sample ID, -N and -K refer to the experiments at Nagoya Institute of Technology (NIT) 353
and Kyoto University (KU), respectively. BosC10-N and Bos26-N data are from 354
Kamiya et al., 2017 and Kamiya et al., 2018, respectively. ‘Softening’ indicates the 355
pressure values where strain softening occurred. 356
357
Fig. 1 (a) Plate configuration of the Japanese Islands. The rectangle indicates the area 358
covered by Figure 1b. (b) Sampling point on the geologic map of the Boso Peninsula 359
(modified from Kamiya et al.12)). 360
361
Fig. 2 Schematic illustrations of the oedometer test apparatus at Kyoto university; (a) 362
Compression system, (b) Test chamber. 363
364
Fig. 3 Void ratio vs log pressure diagram showing the compression index (a) and 365
measurement of consolidation yield stress (b). 366
367
Fig. 4 Consolidation curves; (a) BosC32, (b) BosC10-N and BosC10-K, (c) BosC26-N 368
and BosC26-K. Black line shows the test performed at Kyoto University and gray line 369
shows the test performed in Nagoya Institute of Technology. (d) Stress vs strain diagram 370
of BosC26 focused on the strain softening. 371
372
Fig. 5 X-ray CT images taken before (a, b, c) and after (d, e, f) the consolidation test. 373
The compressive axis is vertical in (b) (c) (e) and (f). The lines in each image show the 374
cutting positions. 375 376
Sample ID Formation Location EquipmentGrain density
(g/cm3)Porosity
(%) Void ratio Ccpc
(MPa)Softening
(MPa)
BosC32 Kiwada East KU 2.58 47.7 0.91 0.49 7.0 12.3BosC10-N Otadai West NIT 2.64 42.7 0.74 0.39 7.6 -BosC10-K Otadai West KU 2.62 40.9 0.69 0.37 8.0 -BosC26-N Ohara East NIT 2.56 49.6 0.99 0.54 9.4 12.3BosC26-K Ohara East KU 2.55 49.3 0.97 0.53 10.3 15.0
Table 1 Basic physical properties and results of the siltstone used in this study. For the sample ID, -N and -K refer to the experiments atNagoya Institute of Technology (NIT) and Kyoto University (KU), respectively. BosC10-N and Bos26-N data are from Kamiya et al., 2017and Kamiya et al., 2018, respectively. ‘Softening’ indicates the pressure values where strain softening occurred.
Chiba
140°
35°
PacificOcean
Mineoka Gp.Miura Gp.
Kazusa Gp.Shimousa Gp.
Hota Gp.(b)
Boso
Pen
insu
la
BosC10BosC26
BosC32
Toky
o Ba
y
Kurotaki Unconformity
Alluvium
(a)
Pacific Plate
0 500 km
130˚ 140˚ 150˚
30˚
40˚
Philippine Sea Plate
Eurasian Plate
North AmericanPlate
Fig. 1b
Kamiya et al., Figure 1
Fig. 1 (a) Plate configuration of the Japanese Islands. The rectangle indicates the area covered by Figure 1b. (b) Sampling point on the geologic map of the Boso Peninsula (modified from Kamiya et al.12)).
Test chamber
Load cell
Displacement transducer
Uniaxial Compression System Pore water pressure meter
Specimen
Consolidation ring
Piston
Teflon
Silicon grease Displacement
transducer
(a) (b)
Drained water volume meter
Close
Kamiya et al., Figure 2
Fig. 2 Schematic illustrations of the oedometer test apparatus at Kyoto university; (a) Compression system, (b) Test chamber.
(a) (b)
0.4
0.6
0.8
1
0.1 1 10 100
Void
ratio
p (MPa)
Cc
Cc’
Cc”
Void
ratio
ee a
e b
pa pb log p
Consolidation curve
A
Cc
B
Kamiya et al., Figure 3
Fig. 3 Void ratio vs log pressure diagram showing the compression index (a) and measurement of consolidation yield stress (b).
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.1 1 10 100
10-N
10-K
Void
ratio
p (MPa)
(a) BosC32 (E-Kiwada) (b) BosC10 (W-Otadai)
(c) BosC26 (Ohara)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 1 10 100
Void
ratio
p (MPa)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 1 10 100
26-N
26-KVoid
ratio
p (MPa)
0
5
10
15
20
25
0 0.02 0.04 0.06 0.08
p (M
Pa)
ε
26-N
26-K
(d) BosC26 (Ohara)
Kamiya et al., Figure 4
Fig. 4 Consolidation curves; (a) BosC32, (b) BosC10-N and BosC10-K, (c) BosC26-N and BosC26-K. Black line shows the test performed at Kyoto University and gray line shows the test performed in Nagoya Institute of Technology. (d) Stress vs strain diagram of BosC26 focused on the strain softening.